WASHINGTON – Senate Democrats see plenty of room for improvement in a sweeping U.S. health care overhaul bill, starting with changes to a tax on high-cost medical insurance policies that could hit middle-class Americans hard.

Senate Finance Committee Chairman Max Baucus, a Democrat, unveiled his much-anticipated bill this week, and senators who have been waiting for months lined up to offer a bevy of contentious changes. One senator said the bill “needs more than just a few tweaks.”

Democrats are concerned about affordability. Republicans almost uniformly oppose the measure and may be loath to hand President Barack Obama a victory on his biggest domestic priority, legislation to rein in skyrocketing health care costs and extend coverage to many of the 50 million uninsured.

The United States is the only industrialized democracy that lacks a comprehensive national health care system. Most Americans rely on health insurance partially subsidized by their employer, and they can lose their family’s coverage if they lose their job.

After months when health care negotiations in the Senate were confined largely to Baucus meeting privately with five other Finance Committee senators to try to craft a bipartisan deal – ultimately without success – the dynamic was noticeably altered Thursday, a day after Baucus produced his long-awaited bill.

Many more senators were in the mix, and many of them had something to say.

“I can find a handful of things that trouble me,” said the Senate’s No. 2 Democrat, Dick Durbin. He cited a new tax on high-value medical insurance plans.

The Baucus plan “needs more than just a few tweaks,” said Sen. Maria Cantwell, a Democrat and member of the Finance Committee, saying she wanted stronger measures to control health care costs over the long term.

“Put it in perspective,” Durbin added. “For months, the debate over health care in the Senate consisted of six people sitting in a room. Now it’s been expanded.

“So we have a lot of people who need to become informed, express themselves, ask for changes if they can,” Durbin said.

Underscoring how every lawmaker is under intense scrutiny, the liberal blog Firedoglake.com planned to begin TV ads in the state of Arkansas next week criticizing two of that state’s Democratic members of Congress for not fully supporting the health care drive. The $78,000 campaign – a significant sum in that state – was aimed at Sen. Blanche Lincoln, a member of the Finance committee, and Rep. Mike Ross, a leader of the House’s moderate Democrats who have sought to keep the bill’s price tag modest.

“Senator Blanche Lincoln and Congressman Mike Ross have stood with the health insurance industry and their allies,” the commercial says, adding, “Stand with Democrats now, or we’ll find someone who will.”

That was happening in earnest Thursday as Baucus convened a full committee meeting on his bill. Senate Democrats met later, and Republicans from the Finance Committee gathered with Senate Minority Leader Mitch McConnell to go over strategy for next week, when Baucus will bring his bill up in committee for amendments – there will be many – and votes.

Democratic concerns focused on the new tax on generous insurance plans and on whether subsidies to help lower-income people buy newly required insurance are ample enough. Liberals also continued to question the absence from Baucus’ proposal of a government-run insurance plan to compete with private industry. That is a feature of four other health bills in Congress but Baucus omitted it as one of numerous gestures meant to win support from Republicans and moderate Democrats. Baucus included nonprofit cooperatives instead.

His bill also would set up new purchasing exchanges in which individuals not otherwise covered could shop for insurance, and it would bar insurance company practices like denying coverage to people who already have health problems. permanent in the House Democrats’ health legislation, which carries a much heftier price tag over $1 trillion.

The release of the bill put new momentum behind Obama’s push for a health care overhaul, and Democratic leaders in the House and Senate hope to move to floor action later in the year. Obama himself pumped up the plan at a rally at the University of Maryland on Thursday, and is set to appear on Sunday television talk shows to push for action.

“There’s now agreement in Congress on about 80 percent of what needs to be done,” Obama told the crowd.

That last 20 percent could still be tough.

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Associated Press writers Ricardo Alonso-Zaldivar and Charles Babington in Washington and Matt Gouras in Montana contributed to this report.